Electron energy spectrum and the Berry phase in a graphite bilayer

We emphasize that there exist four Dirac-type points in the electron energy spectrum of a graphite bilayer near the point K of its Brillouin zone. One of the Dirac points is at the point K , and three Dirac points lie nearby. Each of these three points generates the Berry phase π , while the Dirac point at K gives the phase -π . It is these four points that determine the Berry phase in the bilayer. If an electron orbit surrounds all these points, the Berry phase is equal to 2π .